Microlending, where a bank lends to a small group of people without credit histories, began with the Grameen Bank in Bangladesh, and is widely seen as the creation of Muhammad Yunus, who received the Nobel Peace Prize in recognition of his largely successful efforts. Since that time the modeling of microlending has received a fair amount of academic attention. One of the issues not yet addressed in full detail, however, is the issue of the size of the group. Some attention has nevertheless been paid using an experimental and game theory approach. We, instead, take a mathematical approach to the issue of an optimal group size, where the goal is to minimize the probability of default of the group. To do this, one has to create a model with interacting forces, and to make precise the hypotheses of the model. We show that the original choice of Muhammad Yunus, of a group size of five people, is, under the right, and, we believe, reasonable hypotheses, either close to optimal, or even at times exactly optimal, i.e., the optimal group size is indeed five people.

小额贷款始于孟加拉国的格莱en银行，是一家银行向一小批没有信用记录的人提供贷款的地方，被广泛认为是穆罕默德·尤努斯的创立。穆罕默德·尤努斯获得了诺贝尔和平奖，以表彰他的巨大成功。从那时起，小额贷款的建模受到了相当多的学术关注。但是，尚未详细解决的问题之一是小组规模的问题。然而，使用实验和博弈论方法已经引起了一些关注。相反，我们采用数学方法来解决最佳组大小的问题，其目标是最大程度地降低组的默认概率。为此，必须创建一个具有相互作用力的模型，并精确做出模型的假设。